DOI: 10.1002/actp.1979.010300804. General derivation of the WLF equation from a fluctuation approach to the glass transition

General derivation of the WLF equation from a fluctuation approach to the glass transition

10.1002/actp.1979.010300804

Crossref journal-article

Wiley

Acta Polymerica (311)

Abstract

AbstractIn the frame of a fluctuation approach to the glass transition, it is shown from a scaling argument that the product δ In v δT (≈ 15 K for polymers) is invariant with respect to the temperature or frequency dependence of the glass transition in homogeneous amorphous substances. With the aid of a differential geometry method follows that the very existence of this invariance already determines the form of the lg v‐T‐curves.

Bibliography

Donth, E. (1979). General derivation of the WLF equation from a fluctuation approach to the glass transition. Acta Polymerica, 30(8), 481â485. Portico.

Authors 1

E. Donth (first)

References 19 Referenced 28

10.1021/ja01619a008
{'key': 'e_1_2_1_3_2', 'volume-title': 'Viscoelastic Properties of Polymers', 'author': 'Ferry J. D.', 'year': '1970'} / Viscoelastic Properties of Polymers by Ferry J. D. (1970)
{'key': 'e_1_2_1_4_2', 'first-page': '645', 'volume': '22', 'author': 'Vogel H.', 'year': '1921', 'journal-title': 'Physik. Z.'} / Physik. Z. by Vogel H. (1921)
10.1002/zaac.19261560121
{'key': 'e_1_2_1_6_2', 'first-page': '339', 'volume': '8', 'author': 'Fulcher G. S.', 'year': '1925', 'journal-title': 'J. Amer. Chem. Soc.'} / J. Amer. Chem. Soc. by Fulcher G. S. (1925)
10.1063/1.1696442
10.1007/BFb0022820
10.1002/pssb.2220740156
10.1515/zpch-1977-258129 / Z. phys. Chemie, Leipzig by Donth E. (1977)
{'key': 'e_1_2_1_11_2', 'first-page': '617', 'volume': '25', 'author': 'Donth E.', 'year': '1978', 'journal-title': 'Plaste u. Kautschuk'} / Plaste u. Kautschuk by Donth E. (1978)
10.1063/1.1744141
{'key': 'e_1_2_1_13_2', 'volume-title': 'Statisticheskaya Fizika', 'author': 'Landau L. D.', 'year': '1976'} / Statisticheskaya Fizika by Landau L. D. (1976)
Riechert W.: Diplomarbeit TH Leuna‐Merseburg 1977.
Kamke E.: Differentialgleichungen Lösungsmethoden und Lösungen Bd. II. Leipzig: Akad. Verlagsges. 1959 (chapter 10.3).
10.1021/cr60135a002
10.1007/BFb0111937
{'key': 'e_1_2_1_18_2', 'first-page': '642', 'volume': '24', 'author': 'Donth E.', 'year': '1977', 'journal-title': 'Plaste u. Kautschuk'} / Plaste u. Kautschuk by Donth E. (1977)
10.1002/pol.1975.180131108
10.1002/pol.1977.180150305

Dates

Type	When
Created	22 years, 4 months ago (April 21, 2003, 6:03 p.m.)
Deposited	1 year, 9 months ago (Nov. 2, 2023, 5:49 a.m.)
Indexed	4 months, 1 week ago (April 12, 2025, 12:22 a.m.)
Issued	46 years ago (Aug. 1, 1979)
Published	46 years ago (Aug. 1, 1979)
Published Online	22 years, 4 months ago (April 8, 2003)
Published Print	46 years ago (Aug. 1, 1979)

Funders 0

None

BibTeX

@article{Donth_1979, title={General derivation of the WLF equation from a fluctuation approach to the glass transition}, volume={30}, ISSN={1521-4044}, url={http://dx.doi.org/10.1002/actp.1979.010300804}, DOI={10.1002/actp.1979.010300804}, number={8}, journal={Acta Polymerica}, publisher={Wiley}, author={Donth, E.}, year={1979}, month=aug, pages={481–485} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        4,
        12
      ]
    ],
    "date-time": "2025-04-12T04:22:10Z",
    "timestamp": 1744431730299
  },
  "reference-count": 19,
  "publisher": "Wiley",
  "issue": "8",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2003,
            4,
            8
          ]
        ],
        "date-time": "2003-04-08T00:00:00Z",
        "timestamp": 1049760000000
      },
      "content-version": "vor",
      "delay-in-days": 8651,
      "URL": "http://onlinelibrary.wiley.com/termsAndConditions#vor"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1979,
        8
      ]
    ]
  },
  "abstract": "<jats:title>Abstract</jats:title><jats:p>In the frame of a fluctuation approach to the glass transition, it is shown from a scaling argument that the product \u03b4 In <jats:italic>v</jats:italic> \u03b4<jats:italic>T</jats:italic> (\u2248 15 K for polymers) is invariant with respect to the temperature or frequency dependence of the glass transition in homogeneous amorphous substances. With the aid of a differential geometry method follows that the very existence of this invariance already determines the form of the lg <jats:italic>v\u2010T</jats:italic>\u2010curves.</jats:p>",
  "DOI": "10.1002/actp.1979.010300804",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        4,
        21
      ]
    ],
    "date-time": "2003-04-21T22:03:47Z",
    "timestamp": 1050962627000
  },
  "page": "481-485",
  "source": "Crossref",
  "is-referenced-by-count": 28,
  "title": "General derivation of the WLF equation from a fluctuation approach to the glass transition",
  "prefix": "10.1002",
  "volume": "30",
  "author": [
    {
      "given": "E.",
      "family": "Donth",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "311",
  "published-online": {
    "date-parts": [
      [
        2003,
        4,
        8
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_2_1_2_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1021/ja01619a008"
    },
    {
      "key": "e_1_2_1_3_2",
      "volume-title": "Viscoelastic Properties of Polymers",
      "author": "Ferry J. D.",
      "year": "1970"
    },
    {
      "key": "e_1_2_1_4_2",
      "first-page": "645",
      "volume": "22",
      "author": "Vogel H.",
      "year": "1921",
      "journal-title": "Physik. Z."
    },
    {
      "key": "e_1_2_1_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/zaac.19261560121"
    },
    {
      "key": "e_1_2_1_6_2",
      "first-page": "339",
      "volume": "8",
      "author": "Fulcher G. S.",
      "year": "1925",
      "journal-title": "J. Amer. Chem. Soc."
    },
    {
      "key": "e_1_2_1_7_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1696442"
    },
    {
      "key": "e_1_2_1_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BFb0022820"
    },
    {
      "key": "e_1_2_1_9_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/pssb.2220740156"
    },
    {
      "key": "e_1_2_1_10_2",
      "doi-asserted-by": "crossref",
      "first-page": "977",
      "DOI": "10.1515/zpch-1977-258129",
      "volume": "258",
      "author": "Donth E.",
      "year": "1977",
      "journal-title": "Z. phys. Chemie, Leipzig"
    },
    {
      "key": "e_1_2_1_11_2",
      "first-page": "617",
      "volume": "25",
      "author": "Donth E.",
      "year": "1978",
      "journal-title": "Plaste u. Kautschuk"
    },
    {
      "key": "e_1_2_1_12_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1744141"
    },
    {
      "key": "e_1_2_1_13_2",
      "volume-title": "Statisticheskaya Fizika",
      "author": "Landau L. D.",
      "year": "1976"
    },
    {
      "key": "e_1_2_1_14_2",
      "unstructured": "Riechert W.: Diplomarbeit TH Leuna\u2010Merseburg 1977."
    },
    {
      "key": "e_1_2_1_15_2",
      "unstructured": "Kamke E.: Differentialgleichungen L\u00f6sungsmethoden und L\u00f6sungen Bd. II. Leipzig: Akad. Verlagsges. 1959 (chapter 10.3)."
    },
    {
      "key": "e_1_2_1_16_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1021/cr60135a002"
    },
    {
      "key": "e_1_2_1_17_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BFb0111937"
    },
    {
      "key": "e_1_2_1_18_2",
      "first-page": "642",
      "volume": "24",
      "author": "Donth E.",
      "year": "1977",
      "journal-title": "Plaste u. Kautschuk"
    },
    {
      "key": "e_1_2_1_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/pol.1975.180131108"
    },
    {
      "key": "e_1_2_1_20_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/pol.1977.180150305"
    }
  ],
  "container-title": "Acta Polymerica",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Factp.1979.010300804",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://onlinelibrary.wiley.com/doi/pdf/10.1002/actp.1979.010300804",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        11,
        2
      ]
    ],
    "date-time": "2023-11-02T09:49:11Z",
    "timestamp": 1698918551000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://onlinelibrary.wiley.com/doi/10.1002/actp.1979.010300804"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1979,
        8
      ]
    ]
  },
  "references-count": 19,
  "journal-issue": {
    "issue": "8",
    "published-print": {
      "date-parts": [
        [
          1979,
          8
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1002/actp.1979.010300804"
  ],
  "URL": "http://dx.doi.org/10.1002/actp.1979.010300804",
  "relation": {},
  "ISSN": [
    "0323-7648",
    "1521-4044"
  ],
  "subject": [],
  "container-title-short": "Acta Polymerica",
  "published": {
    "date-parts": [
      [
        1979,
        8
      ]
    ]
  }
}